.TH  ZCGESV 1 "November 2008" " LAPACK PROTOTYPE driver routine (version 3.2) " " LAPACK PROTOTYPE driver routine (version 3.2) " 
.SH NAME
ZCGESV - computes the solution to a complex system of linear equations  A * X = B,
.SH SYNOPSIS
.TP 19
SUBROUTINE ZCGESV(
N, NRHS, A, LDA, IPIV, B, LDB, X, LDX, WORK,
.TP 19
.ti +4
+
SWORK, RWORK, ITER, INFO )
.TP 19
.ti +4
INTEGER
INFO, ITER, LDA, LDB, LDX, N, NRHS
.TP 19
.ti +4
INTEGER
IPIV( * )
.TP 19
.ti +4
DOUBLE
PRECISION RWORK( * )
.TP 19
.ti +4
COMPLEX
SWORK( * )
.TP 19
.ti +4
COMPLEX*16
A( LDA, * ), B( LDB, * ), WORK( N, * ),
.TP 19
.ti +4
+
X( LDX, * )
.SH PURPOSE
ZCGESV computes the solution to a complex system of linear equations
   A * X = B,
where A is an N-by-N matrix and X and B are N-by-NRHS matrices.
ZCGESV first attempts to factorize the matrix in COMPLEX and use this
factorization within an iterative refinement procedure to produce a
solution with COMPLEX*16 normwise backward error quality (see below).
If the approach fails the method switches to a COMPLEX*16
factorization and solve.
.br
The iterative refinement is not going to be a winning strategy if
the ratio COMPLEX performance over COMPLEX*16 performance is too
small. A reasonable strategy should take the number of right-hand
sides and the size of the matrix into account. This might be done
with a call to ILAENV in the future. Up to now, we always try
iterative refinement.
.br
The iterative refinement process is stopped if
.br
    ITER > ITERMAX
.br
or for all the RHS we have:
.br
    RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX
.br
where
.br
    o ITER is the number of the current iteration in the iterative
      refinement process
.br
    o RNRM is the infinity-norm of the residual
.br
    o XNRM is the infinity-norm of the solution
.br
    o ANRM is the infinity-operator-norm of the matrix A
.br
    o EPS is the machine epsilon returned by DLAMCH(\(aqEpsilon\(aq)
The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00
.br
respectively.
.br
.SH ARGUMENTS
.TP 8
N       (input) INTEGER
The number of linear equations, i.e., the order of the
matrix A.  N >= 0.
.TP 8
NRHS    (input) INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B.  NRHS >= 0.
.TP 8
A       (input or input/ouptut) COMPLEX*16 array,
dimension (LDA,N)
On entry, the N-by-N coefficient matrix A.
On exit, if iterative refinement has been successfully used
(INFO.EQ.0 and ITER.GE.0, see description below), then A is
unchanged, if double precision factorization has been used
(INFO.EQ.0 and ITER.LT.0, see description below), then the
array A contains the factors L and U from the factorization
A = P*L*U; the unit diagonal elements of L are not stored.
.TP 8
LDA     (input) INTEGER
The leading dimension of the array A.  LDA >= max(1,N).
.TP 8
IPIV    (output) INTEGER array, dimension (N)
The pivot indices that define the permutation matrix P;
row i of the matrix was interchanged with row IPIV(i).
Corresponds either to the single precision factorization
(if INFO.EQ.0 and ITER.GE.0) or the double precision
factorization (if INFO.EQ.0 and ITER.LT.0).
.TP 8
B       (input) COMPLEX*16 array, dimension (LDB,NRHS)
The N-by-NRHS right hand side matrix B.
.TP 8
LDB     (input) INTEGER
The leading dimension of the array B.  LDB >= max(1,N).
.TP 8
X       (output) COMPLEX*16 array, dimension (LDX,NRHS)
If INFO = 0, the N-by-NRHS solution matrix X.
.TP 8
LDX     (input) INTEGER
The leading dimension of the array X.  LDX >= max(1,N).
.TP 8
WORK    (workspace) COMPLEX*16 array, dimension (N*NRHS)
This array is used to hold the residual vectors.
.TP 8
SWORK   (workspace) COMPLEX array, dimension (N*(N+NRHS))
This array is used to use the single precision matrix and the
right-hand sides or solutions in single precision.
.TP 8
RWORK   (workspace) DOUBLE PRECISION array, dimension (N)
.TP 8
ITER    (output) INTEGER
< 0: iterative refinement has failed, COMPLEX*16
factorization has been performed
-1 : the routine fell back to full precision for
implementation- or machine-specific reasons
-2 : narrowing the precision induced an overflow,
the routine fell back to full precision
-3 : failure of CGETRF
.br
-31: stop the iterative refinement after the 30th
iterations
> 0: iterative refinement has been sucessfully used.
Returns the number of iterations
.TP 8
INFO    (output) INTEGER
= 0:  successful exit
.br
< 0:  if INFO = -i, the i-th argument had an illegal value
.br
> 0:  if INFO = i, U(i,i) computed in COMPLEX*16 is exactly
zero.  The factorization has been completed, but the
factor U is exactly singular, so the solution
could not be computed.
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